During the night of August 31 a group of German soldiers, dressed as Poles, attack the German radio station in the border town of Gleiwitz. They have brought with them a German criminal, taken for the purpose from a concentration camp. They shoot him and leave his body as evidence of the night's dark deeds.

Berlin radio broadcasts to the world the news of this act of Polish aggression, together with details of the necessary German response. In the early hours of the morning of September 1 Hitler's tanks move into Poland. His planes take off towards Warsaw on the first bombing mission of a new European war.

After a final desperate day of diplomacy, attempting even at this late stage to find a peaceful solution, Chamberlain and Daladier each sends an ultimatum to Hitler. When no answer is received, both nations declare war on September 3.

The Polish army, airforce and civilian population put up a brave resistance to massive German force - increased, from September 17, by a Russian invasion from the east. Within a few weeks 60,000 Polish soldiers and 25,000 civilians die. By September 28 Warsaw has fallen. Poland is once again partitioned, with an eastern slice going to Russia (as so recently agreed in Moscow) and the lion's share to Germany.

The Phoney War: 1939-1940

In France and Britain the immediate aftermath of the declaration of war is a return to the defensive tactics of World War I. The French rush troops to the Maginot Line, an elaborate complex of concrete fortifications connected by underground railway lines, which has been constructed along the Franco-German border between 1929 and 1938. (It is named after André Maginot, minister of war from 1929 to 1931.)

France's border with Belgium, running northwest to the sea, is not similarly protected. So, as in World War I, a British Expeditionary Force is immediately sent across the Channel to dig in along this line.

Here the troops of both nations await attack from the conqueror of Poland. But nothing happens.

It is not that Hitler is inactive against his new enemies. He is energetically demonstrating, with the deployment of his U-boats (Unterseebooten, or submarines), that Britain can no longer rely on her famed mastery of the seas. The aircraft carrier Courageous is sunk at sea in September, the battleship Royal Oak is torpedoed at anchor in Scapa Flow in October. Hitler also has a devastating new weapon to unveil - the magnetic mine, dropped into the sea from the air to cling to a passing vessel and explode. Inevitably indiscriminate, one such mine sinks the Dutch passenger liner Simon Bolivar in November.

Nor is there a lack of conflict in Europe. Stalin, assured of a free hand with Finland by the terms of his nonaggression pact with Hitler, sends troops across the Finnish border in November 1939 (provoking the Russo-Finnish war, also known as the Winter War, in which Finland resists her large neighbour with magnificent resolve). And in early April 1940 the French and British finally agree on their first joint offensive. They will send troops to seize the Norwegian North Sea ports, even though Norway is neutral. The strategic reason is the need to cut the supply of iron ore from Swedish mines to Germany. But they delay in putting the plan into action.

Meanwhile on the western front all is quiet.

As a result the war acquires in Britain and France a name suggesting a dangerous sense of relaxation. In Britain it is known as the Phoney War, in France le Drole de Guerre (the Joke War). By the spring of 1940 the western nations have been able to spend eight useful months building up their armaments. On April 5 Chamberlain is sufficiently confident to declare to the house of commons that one thing is now certain - Hitler has 'missed the bus'.

Four days later a German fleet of warships invades Denmark and Norway. All the important harbours of these two neutral nations are rapidly occupied. Within days British and French troops are on hand to assist the Norwegian resistance. But they have arrived too late and little is achieved.

Enter Churchill: 1940

The military failure in Norway heightens dissatisfaction in Britain with Chamberlain's conduct of the war. On May 7-8 he narrowly survives a censure debate in the house of commons (notable for Leo Amery's revival of Cromwell's famous words 'You have sat too long here for any good you have been doing... In the name of God, go!'). Then, on May 10, alarming news from the continent sets the seal on his term as leader.

In the early hours of that morning German divisions smash their way into the Netherlands and Belgium. In this new crisis Chamberlain realizes that an all-party government is essential. But the Labour party refuses to serve under a man associated so strongly with appeasement.

The leading candidate to succeed Chamberlain in these circumstances is a controversial figure waiting in the wings. Winston Churchill, after a brilliant early career (first as soldier and author, subsequently in several high cabinet roles), has been on the sidelines during the 1930s because of his implacable opposition to appeasement. He has described Chamberlain's 'peace with honour' at Munich as 'a total and unmitigated defeat'.

Pugnacious and inspirational, Churchill is the ideal man for the crisis now facing Europe. Appointed prime minister on the very day when Hitler's troops move west into the Netherlands and Belgium, his first task is to confront the famous German blitzkrieg.

Netherlands and Belgium: 1940

When German tanks cross the border into the Netherlands, Luxembourg and Belgium, in the early hours of May 10, it is the start of the most dramatic demonstration of the new German strategy of blitzkrieg ('lightning war'). The technique has been used with devastating success against Poland in September 1939, bringing the fall of Warsaw within just four weeks. But on the western front the defending forces are stronger, the terrain of rivers and canals more difficult, and the speed of success and the range of offensive tactics even more astonishing.

German troops arrive out of the blue (dropping by parachute, landing in gliders) to seize strategic bridges, while the armoured corps and the infantry move at unimagined speed to separate the defending forces.

In the Netherlands, within two days of the start of the invasion, a German division reaches the coast near Rotterdam. The following day, May 13, Queen Wilhelmina and her government depart for England. On the 14th the caretaker government surrenders to the invader.

In Belgium the agony lasts a little longer, involving French and British armies as well as the Belgian defenders of the country. On May 14-15 the German advance is briefly checked, but at the same time a development to the south is making this almost irrelevant. Another Germany army, driving west through Luxembourg, reaches the Meuse by the evening of May 12. If the Germans can cross the river, there is a danger that they will cut off the Allied armies to the north.

A thousand German aircraft are on hand to assist this river crossing. Ceaseless attacks by divebombers demoralize the French defenders on the south bank of the river near Sedan, while German infantry cross in inflatable boats. Once on the opposite bank, they establish bridgeheads to which tanks can be safely ferried. By May 15 the vanguard, under Heinz Guderian, is already moving on. On May 17 Guderian crosses the Oise. On May 20 he reaches Abbeville and the coast. Just nine days ago his men were in Germany.

To the north the Belgians are still holding out, though not for long (their surrender comes on May 27). But large numbers of British and French troops are now trapped. Their only escape is westwards to the sea. And the Germans are moving up the coast to complete the encirclement.

Dunkirk: 1940

One part of the Allied force at risk of being captured in Belgium is the British Expeditionary Force. Sent from Britain in September 1939, the BEF has spent the winter dug in along the Franco-Belgian border. Sharing the present danger with them is the French 1st Army.

Even before the fall of Belgium, Churchill decides that the only safe course is to evacuate the BEF. In these desperate circumstances the admiralty enlists the help of every small craft in southern England capable of crossing the Channel and going into shallow water off a beach. The result is the most improbable of flotillas, but one which - in conjunction with the ships of the British navy - achieves an astonishing feat, far exceeding expectations.

Even so, but for an intervention by Hitler, the miracle of Dunkirk would not have happened. It is the most northerly port in France, the last before the Belgian border. With Belgium about to capitulate, the British and French forces must cross the border and reach Dunkirk to have a chance of escape. They are at least two days away, on May 23, when a German army moving north up the coast arrives near the town. But it stops short. Hitler himself, on May 24, orders its commander to hold back.

The reason is not clear. It is possible he wants to safeguard his army for the more important drive south to Paris. It may be that he feels Britain will be less likely to make peace if humiliated by the capture of so many troops.

Another reason may be that Goering, in command of the German air force, is urging Hitler to leave it to his pilots to prevent any British rescue attempt. Whatever Hitler's motive, he changes his mind three days later. But by then it is too late. The British and French have reached Dunkirk and have constructed defences.

On May 26 the first troops are embarked. The following day the harbour is partly disabled by German bombs, so the evacuation is extended to a long stretch of beach east of the town, where the civilian craft - the fishing smacks, private cruisers, river ferries - come into their own. For ten days, until June 4, under a hail of bombs and beneath a constant battle between German and British planes, some 860 vessels ply back and forth with their precious cargo.

Some 200,000 British and 140,000 French troops are safely ferried across (and another 200,000 Allied troops are taken on board from the Brittany peninsula in subsequent weeks). It is not a victory, but it is a sensational avoidance of defeat. Churchill greets it in his most pugnacious mood, with his famous declaration to the House of Commons that 'We shall fight on the beaches...' And he goes out of his way to praise the young men of the airforce fighting above Dunkirk, implying with considerable foresight that the safety of the country may lie in their hands.

For Hitler too it may not be a victory, but he has had victory enough in the past four weeks. A million Allied soldiers have been captured by his armies since May 10. And now he has his sights on Paris.

The fall of France: 1940

On June 5, the day after the last departures from Dunkirk, the German army turns its attention southwards. Erwin Rommel, whose panzer division has spearheaded the rapid German thrust to the coast, is now again in the vanguard with his tanks. By June 9 the Germans have taken Rouen and crossed the Seine. On June 14 they enter Paris. The French government withdraws to Bordeaux, but the Germans press on relentlessly. By June 16 they are in the Rhone valley.

Meanwhile a similar drive southwards on the eastern front makes the famous Maginot Line redundant. Moving behind it to reach the Swiss frontier, the Germans seal off the French divisions which have been attempting to hold these eastward-facing fortifications.

This impressive sequence of events tempts a newcomer into the war. In spite of their Axis agreement, Mussolini declined in September 1939 to commit Italy to war as an ally of Germany. Now, nine months later, he realizes that if he is to hope for any of the spoils of victory he had better get into the fray. Just in time, on June 10, he declares war on France and Britain. Within less than a week, on June 16, the French ask for an armistice. Mussolini has not yet managed to launch an attack on southeastern France, but he does so on June 20 - two days before France and Germany sign their armistice.

There has been much debate within France whether to seek an armistice or to accept the fall of France and fight on from north Africa.

The premier, Paul Reynaud, has long been anti-appeasement and now argues that France must fight on as Britain's ally. But he is in the minority. On June 16 he resigns. He is followed by a figure from the past, Philippe Pétain, one of France's most distinguished and popular commanders from World War I. Pétain immediately asks for an armistice.

Before dictating terms, Hitler meets in Munich his very recent companion in arms, Mussolini, to discuss what is to be demanded. Mussolini has wildly ambitious plans. In pursuit of his dream of dominating the Mediterranean, he wants Italy to annexe all French imperial possessions in north Africa together with Corsica and the coast of France herself as far west as Nice.

But Hitler is in more practical mood. His main concern is to ensure that France does not go on fighting against him as an ally of Britain (with whom he has not yet given up hope of coming to amicable terms). So he intends only to occupy the northern two thirds of France, already in possession of his armies. He will not even commandeer the powerful French fleet and airforce, insisting merely that they remain non-combatant (much of the fleet is subsequently destroyed by the British). Italy is to have just the tiny bit of southeastern France which her troops have managed to capture during June 20-22.

But if the terms of the armistice are calculated to minimize France's humiliation, the signing of the treaty is stage-managed with precisely the opposite intention.

This is to be the moment when Hitler avenges Germany's humiliation of the armistice at the end of World War I, and he plans it with his usual theatrical flair. The railway carriage in which that armistice was signed has been in a Paris museum. It is now brought to the precise place, at Rethondes, used on the previous occasion. Hitler arrives in person on June 22 to savour his triumph. He even sits in the very chair used by Foch. Then he travels to Paris to see the famous sights. The conqueror plays the tourist (it is his first visit).

The area left to France, officially neutral under Pétain but in effect a German puppet state, has a curving northern boundary from the Swiss border to the Pyrenees. Vichy is selected as the capital, and the region becomes known as Vichy France.

Yet France remains in the war in a different guise. On June 6 Reynaud has brought into his government a young brigadier general, Charles de Gaulle, as undersecretary of state for war. When the armistice is requested, on June 16, de Gaulle crosses to Britain.

From there, on June 18, four days before the armistice is signed, he makes a famous radio broadcast to the people of France. He urges them to continue the fight, and declares himself to be the leader of the Free French. Until the liberation of France, in September 1944, he remains in London as the symbol of French resistance (and frequently as something of a thorn in the side of his more powerful political ally, Winston Churchill).

Battle of Britain and the Blitz: 1940

With the fate of France settled by the middle of June, Hitler turns his attention to Britain. His first task is to achieve a position in which he can ferry troops across the Channel. Dunkirk has proved (if proof were needed) that this will be impossible without command of the air.

On July 16 Hitler orders his commanders to prepare for an invasion of Britain, codenamed Operation Sea Lion. But during June there have already been the first attempts to assert control of the Channel. Bombing raids are launched against British convoys. On July 6 German bombers risk a daylight bombing raid as far inland as the barracks at Aldershot, where several soldiers are killed. On July 10 seventy German bombers attack docks in South Wales.

In these attacks the Germans are taking a major risk. The British planes are as good as their German equivalents, if not better. The Hurricane can match any German fighter except the Messerschmitt 109 - and this is equalled by Britain's newest and fastest machine, the Spitfire. Over British soil the Spitfire has the great advantage of fighting much closer to its fuel supply than the Messerchmitt. And British pilots, bailing out over home territory, can fly and fight again whereas the Germans face only captivity.

Moreover the British enjoy one other crucial advantage. Since 1938 tall thin masts have been constructed at intervals along the British coast. Receiving and transmitting radio signals, they are the world's most advanced application of the new technology of radar.

So the British can tell when and where an attack is coming (a significant fact of which the Germans are at first unaware). Even so, with German superiority in the number of planes available, the dogfights and bombing raids of the summer of 1940 are a period of extreme peril for Britain. In recognition of its decisive nature, this struggle in the air becomes known as the Battle of Britain.

During August, the most intense period of the campaign, the German purpose is to bomb the radar masts and the airfields of Fighter Command. Sometimes as many as 1500 German planes are involved in a single day's assault. But they lose more of their planes than the British, and they fail in their aim. The radar masts stand. The Hurricanes and the Spitfires keep taking off.

In September the German policy changes. Night-time bombing raids on large cities, to destroy the nation's infrastructure and to demoralize the population, now become the main thrust of the attack. The first raid is on London during the night of September 7. The event is described in the Daily Express of September 9 as 'blitz bombing', treating it as part of Germany's strategy of blitzkrieg.

The name sticks. Throughout that winter London and other British cities suffer the Blitz. Sometimes, as in Coventry on November 14, the weight of explosives is such that the technique becomes known as carpet bombing (of which the most intense example, later in the war, is the controversial British attack on Dresden during the night of 13 February 1945).

But the Blitz fails to break the spirit of Britain's city-dwellers. Even by the time it begins, it seems evident that Hitler will not be able to achieve mastery of the air around or over Britain. As early as August 20, after Britain's young fighter pilots have consistently had the better of their opponents in an intense series of air battles over the previous week, Churchill makes his famous speech to the House of Commons which gives them their lasting name - the Few, to whom so many owe so much.

But if Germany has failed to control the air, the outcome of a much longer battle for the shipping routes of the Atlantic is as yet far from undecided.

War in the Atlantic: 1939-1941

As in World War I, Germany's best chance of starving Britain of supplies is through submarine warfare against merchant ships in the Atlantic. The danger is immediately evident as soon as Britain declares war. On the very first day of the conflict, 3 September 1939, a German U-boat sinks the British passenger liner Athenia with the loss of 112 civilian lives.

This is against Hitler's specific order that no passenger vessel shall be attacked (remembering the damage done by the sinking of the Lusitania), but on the military front German U-boats also make an immediate impact. On September 14 a German torpedo strikes the aircraft carrier Ark Royal. It fails to explode. But three days later another British aircraft carrier is less fortunate.

On September 17 a German U-boat scores a direct hit on the Courageous. The carrier sinks in fifteen minutes with the loss of 518 men. And on October 14 a U-boat achieves an even more sensational feat. Its captain, with great bravado, steers his way between the ships guarding the entrance to the supposedly secure anchorage of Scapa Flow. Once inside, he torpedoes and sinks the battleship Royal Oak, killing 833 men. He then succeeds in evading his pursuers to arrive back, a hero, in German waters.

But the main U-boat target is merchant ships carrying supplies, of which 114 are sunk before the end of 1939. As in World War I, the solution is convoys. But Britain lacks sufficient escort vessels to cover the entire Atlantic crossing. Convoys travel unprotected in mid-ocean.

This deficiency is not crucial in 1939 and early 1940, when the U-boats have to travel from their bases in the Baltic round the north coast of Scotland before they reach the Atlantic (the Channel, by far the shorter route, being densely seeded with British mines).

But with the fall of France, in June 1940, a long stretch of captured coastline provides much more convenient home ports for the Atlantic hunters. Their range suddenly extends far beyond what the British destroyers can cover. For the rest of that year the tonnage of British ships sunk in the Atlantic is on average five times higher each month than it was in May. And these are the very months when another struggle for survival is taking place in the air, in the Battle of Britain.

The Germans, in this same summer, use another effective device to prey on any unescorted Atlantic shipping. Six naval ships are disguised, with cranes and cargo on their decks, to look like unarmed merchant vessels. Trusted by their unsuspecting victims, they despatch them easily at close quarters.

But October 1940 brings the first practical help from the USA. In exchange for the use of eight British bases in the western hemisphere, Britain receives fifty antiquated but serviceable US destroyers for Atlantic duty. They enable the convoys to be escorted further into the danger zone in mid-ocean. And the US soon finds other ways to help the beleaguered British.